A $ (k, n) $ threshold secret image sharing (SIS) scheme divides a secret image into $ n $ shadows. One can reconstruct the secret image only when holding $ k $ or more than $ k $ shadows but cannot know any information on the secret from fewer than $ k $ shadows. Based on this characteristic, SIS has been widely used in access control, information hiding, distributed storage and other areas. Verifiable SIS aims to prevent malicious behaviour by attackers through verifying the authenticity of shadows and previous works did not solve this problem well. Our contribution is that we proposed a verifiable SIS scheme which combined CRT-based SIS and $ (2, n+1) $ threshold visual secret sharing(VSS). Our scheme is applicable no matter whether there exists a third party dealer. And it is worth mentioning that when the dealer is involved, our scheme can not only detect fake participants, but also locate dishonest participants. In general, loose screening criterion and efficient encoding and decoding rate of CRT-based SIS guarantee high-efficiency shadows generation and low recovery computation complexity. The uncertainty of the bits used for screening prevents malicious behavior by dishonest participants. In addition, our scheme has the advantages of lossless recovery, no pixel expansion and precise detection.
Citation: Jingju Liu, Lei Sun, Jinrui Liu, Xuehu Yan. Fake and dishonest participant location scheme in secret image sharing[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2473-2495. doi: 10.3934/mbe.2021126
A $ (k, n) $ threshold secret image sharing (SIS) scheme divides a secret image into $ n $ shadows. One can reconstruct the secret image only when holding $ k $ or more than $ k $ shadows but cannot know any information on the secret from fewer than $ k $ shadows. Based on this characteristic, SIS has been widely used in access control, information hiding, distributed storage and other areas. Verifiable SIS aims to prevent malicious behaviour by attackers through verifying the authenticity of shadows and previous works did not solve this problem well. Our contribution is that we proposed a verifiable SIS scheme which combined CRT-based SIS and $ (2, n+1) $ threshold visual secret sharing(VSS). Our scheme is applicable no matter whether there exists a third party dealer. And it is worth mentioning that when the dealer is involved, our scheme can not only detect fake participants, but also locate dishonest participants. In general, loose screening criterion and efficient encoding and decoding rate of CRT-based SIS guarantee high-efficiency shadows generation and low recovery computation complexity. The uncertainty of the bits used for screening prevents malicious behavior by dishonest participants. In addition, our scheme has the advantages of lossless recovery, no pixel expansion and precise detection.
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Jingju Liu, Lei Sun, Jinrui Liu, Xuehu Yan. Fake and dishonest participant location scheme in secret image sharing[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2473-2495. doi: 10.3934/mbe.2021126
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